Related papers: Higher order Matching Pursuit for Low Rank Tensor …
In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…
In recent years, the success of deep learning has inspired many researchers to study the optimization of general smooth non-convex functions. However, recent works have established pessimistic worst-case complexities for this class…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…
Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Low-rank tensor approximation error bounds are proposed for the case of noisy input data that depend on low-rank representation type, rank and the dimensionality of the tensor. The bounds show that high-dimensional low-rank structured…
Multitask learning (MTL) leverages task-relatedness to enhance performance. With the emergence of multimodal data, tasks can now be referenced by multiple indices. In this paper, we employ high-order tensors, with each mode corresponding to…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…